JP2017199084A - Structure design assist device capable of discovering dynamic weak point of structure using inductive force - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a device for calculating an inductive force acting in a direction separate from the direction of load as one index for specifying a bent portion where the function to transmit a load cannot be exhibited, and for consideration of whether or not it is easily deformable, in computer-aided numerical analysis of the dynamic characteristic of a structure.SOLUTION: A numerical analysis device of the present invention includes: means for calculating an inductive force vector acting in a direction separate from the direction of load in each analysis element of a structure when a load is applied to a numerical model of the structure; means for calculating the non-corrected displacement of each analysis element against the load; means for calculating the corrected displacement of each analysis element when a corrected load obtained by subtracting the inductive force vector from the load is applied to the structure; means for comparing the non-corrected displacement and corrected displacement of each analysis element and evaluating the contribution of the inductive force vector; and means for outputting or displaying the contribution of the inductive force vector.SELECTED DRAWING: Figure 7

Description

  The present invention relates to a numerical analysis apparatus for mechanical properties of a structure using a computer. More specifically, the present invention relates to design of a structure through analysis of stress distribution of the structure using numerical analysis such as a finite element method. The present invention relates to a structure design support apparatus capable of obtaining useful information.

  With the development of numerical computation technology in computers, the mechanical or mechanical properties of structures such as vehicle bodies, various machine tools, buildings, etc. are numerically analyzed by the finite element method using computers, etc. The information obtained there is used for designing the structure. According to the analysis method of the mechanical or mechanical characteristics of the structure by the numerical analysis by the computer, whether or not the structure has the required characteristics in the design stage before the actual structure is manufactured. This is advantageous in that it can be grasped and a design change can be made to provide the structure with such required characteristics. Various techniques have been proposed as a technique for performing numerical analysis of the mechanical or mechanical characteristics of a structure using such a computer. For example, in Patent Document 1, when obtaining an optimal structure shape that satisfies an objective function under a predetermined constraint condition using a phase optimization method, the result of structural analysis of the finite element method, When the rigidity of the structure is lower than the constraint, it is proposed to set the rigidity of the structure virtually high and allow a margin before phase optimization, thereby reducing the number of man-hours required for analysis. ing. In Patent Document 2, in the numerical analysis of the load path at the time of collision of the passenger car structure that deforms nonlinearly, the portion where the linear elastic displacement is dominant is replaced with a complete linear elastic body, and the linear elasticity at the time of the collision is changed. A method has been proposed in which load data in body deformation is calculated by a finite element method to analyze a load path. Patent Document 3 discloses a component for stiffening based on the result of calculating the curvature of a component by numerical analysis when quantitatively evaluating the deformation of the component at the time of loading a structure in the vehicle structure. It proposes to select parts that reduce the plate thickness. Furthermore, in patent document 4, when calculating the stress which generate | occur | produces between layers when a bending stress is provided with respect to a laminated material, surface stress is calculated from the curvature radius and principal stress obtained by the finite element method for every layer to overlap. It is proposed that the maximum tensile stress between the layers is calculated by subtracting them and used for the design to reinforce the part that is easily separated.

JP2008-40528 JP2013-8259A JP2013-92835A JP2004-110793 JP 2005-38211 A

  By the way, in a structure having a curved portion, when a load is applied, depending on the direction of the load, a portion in a state where the function of transmitting the applied load is not sufficiently exhibited in the curved portion. Can occur. For example, as illustrated in FIG. 8A, in the figure, a beam-like structure having an H-shaped cross section (two parallel plates from the beginning) in which a middle plate is interposed between upper and lower curved plates in a direction perpendicular to the plate surface. When a load that generates a bending moment is applied to the beam-like structure in which the plate is curved in the direction perpendicular to the surface), the degree of bending is as shown in FIG. Further, as shown schematically in FIG. 8C, the upper and lower curved plates are also deformed so that both edges approach each other. The deformation of both edges of the upper and lower curved plates that are deformed in the direction approaching each other is due to the load that generates the bending moment applied to the illustrated beam-like structure. It can be said that it does not fulfill the function of supporting the applied load, that is, it is a part that deforms without fully exhibiting the function of transmitting the load. In FIG. 8B, when the stress distribution shown by shading (obtained by the finite element method) is seen, it is understood that almost no stress is generated in both edge portions. This indicates that a force escape caused by an induced force, which will be described later, has occurred, and the function of transmitting a load cannot be fully exhibited. It is possible to improve the strength and rigidity by proper reinforcement.

  According to the numerical analysis method using the finite element method or the like by the above computer, the stress or strain in the structure when a force is applied to the structure as shown by the stress distribution shown by the shading in FIG. When there is a part that does not perform the function of transmitting a load in the structure, that is, when there is a part with low stress, by referring to the stress distribution, The range can be specified. However, in the case of a numerical analysis method using a conventional finite element method or the like, it is generally difficult to specify the reason when there is a part that does not perform the function of transmitting a load in the structure, and the reason is specified. Otherwise, it will be difficult to find a design change method for improving the structure. For example, in the case of the example shown in FIG. 8B, first, the stress distribution is calculated by the finite element method, and the deformation analysis is performed. As a result, a portion having a small stress that does not contribute to load transmission is deformed. However, it is difficult to specify the cause of such deformation by simply referring to the stress distribution and the degree of deformation. In addition, when a method for analyzing a load path (such as Patent Document 2) is applied to such an example, a portion that does not perform a function of transmitting a load is not displayed at all, or When a method for automatically optimizing the shape of the structure (Patent Document 3, etc.) is applied, the part that does not perform the function of transmitting the load will be scraped off, and the structure is added with appropriate reinforcement. It is not optimized to improve the direction.

  Regarding the deformation of the portion where the function of transmitting the load when the load is applied in the structure having the curved portion as described above, the inventor of the present invention has made such deformation in Japanese Patent Application No. 2015-0099978. However, depending on the direction of the load applied to the curved portion, a force acting in a direction different from the direction in which the load is transmitted (a direction parallel to the principal stress of the stress at the part) is generated. I found out. The force acting in a direction different from the transmission direction of the load and its vector are defined as “inductive force” and “inductive force vector”, the magnitude of which is the direction of the main stress of each part in the structure. It can be expressed by the rate of change (differential value) of the, and it can be used as one index for consideration of whether or not it is easy to deform and specify a part where the function of transmitting the load is not exhibited Indicated.

  Regarding the inductive force as described above, when considering the location of a structure that does not function to transmit the load based on the inductive force and ease of deformation, not only refer to the distribution of inductive force but also the inductive force. It would be even more advantageous if the influence of the structure on the displacement of the structure can be grasped more quantitatively. In the above application, the “inductive force vector” is calculated by differential calculation of principal stress obtained numerically in the numerical model of the structure to be analyzed. The “vector” can be directly calculated from the applied load or displacement without explicitly calculating the main stress.

  Thus, an object of the present invention is to provide a novel quantitative analysis of the influence of the induction force on the displacement of the structure when analyzing the mechanical characteristics of the structure by numerical analysis using a computer. It is to provide an index, a calculation method thereof, and a new calculation method of “inductive force”.

  According to the present invention, one of the above problems is a numerical analysis apparatus for mechanical properties of a structure using a computer, in which the structure has a numerical model of a structure having a plurality of analysis elements. When a load is applied, a means for calculating an induction force vector acting in a direction different from the direction of the load in each analysis element, and a load is applied to the structure in the numerical model of the structure In the case where a correction load obtained by subtracting the induced force vector from the load is applied to the structure in the numerical model of the structure and the means for calculating the uncorrected displacement that occurs in each of the analysis elements Means for calculating a correction load generated in each of the analysis elements, means for calculating an index value representing the contribution of the induction force vector based on the uncorrected displacement and the correction displacement in each of the analysis elements, and the induction force vector The index value representing the contribution of It is achieved by a device comprising means for displaying.

In the above configuration, the “structure” is a structure such as a body of a vehicle, various mechanical devices, buildings, or arbitrary members constituting them, and a structure in which stress can be defined. It may be. “Numerical analysis” may typically be a finite element method, but is not limited thereto, and is set at an arbitrary part of the structure when an arbitrary load is applied to the structure. Any analysis method capable of calculating the stress and / or displacement of a plurality of analysis elements may be used. "Inductive force vector" is the derivative of each principal stress in its corresponding principal axis direction when the structure is an elastic body to which solid mechanics is applied and the differential value of stress can be calculated in any direction. It is defined as a vector whose components are values. Further, the numerical model of the structure is an elastic body having a shell structure, and the structure is divided into a plurality of analysis elements, and each analysis element is a polygonal element defined by three or more nodes. In this case, since the differential value of the stress in the thickness direction is not calculated, the inductive force vector includes the component Fn in the thickness direction for each node of each analysis element, the curvature matrix Q _ij of each analysis element, and the stress tensor σ _ij And
Fn = Σ _i Σ _j Q _ij σ _ij (A)
Also represented by (Here, Σ _i and Σ _j represent the sum of i and j.)

  In the above-described configuration of the numerical analysis device for the mechanical characteristics of the structure of the present invention, first, the “inductive force vector” described above is calculated. In short, the “inductive force vector” is, as will be described in more detail later, when a load in a direction along the bending direction (circumferential direction) is applied to the curved portion of the structure. This corresponds to a force (unit is a force per volume) generated in a direction perpendicular to the load. That is, this “inductive force vector” is an amount that can be referred to as an index value of the magnitude of a force acting in a direction different from the load applied to the structure. Further, in the numerical analysis device of the present invention, the displacement (“non-non-zero”) generated in each of the analysis elements in a state where the induced force vector is generated, that is, in a state where a load causing the induced force vector is applied. ) And a displacement ("" that is generated by subtracting the induced force vector from the load (referred to as "corrected load")) in each of the analysis elements in a state where the structure is applied. This is calculated as an index value representing the contribution of the induction force vector based on the “corrected displacement” and “uncorrected displacement”.

  In the above configuration, the state in which the “correction load” is applied is a state in which the induction force vector is subtracted in the state in which the initial load is applied, and thus the “correction displacement” in that state. Is assumed to be the displacement with the induction force vector removed. In fact, if the induction force vector is removed from the initial applied load, the displacement at the site where the induction force was not significantly generated in the structure may also change. There may be cases where the displacement due to the induced force vector is not simply removed. However, by comparing the “corrected displacement” with the “uncorrected displacement”, the influence of the induced force vector on the structure is affected. It will be useful in considering what it is doing. Therefore, as described above, in order to compare the uncorrected displacement and the corrected load, an index value representing the contribution of the induced force vector based on “corrected displacement” and “unmodified displacement” (referred to as “inductive force influence index value”). ) Is calculated and output or displayed. When an index value in a comparison between “corrected displacement” and “uncorrected displacement” is large in a certain analysis element, the load transmission function is not fully exhibited in that portion. Therefore, it can be determined that the portion is a portion where the force is “running away” (acts in a direction different from the direction in which the applied load is expected).

  As the “inductive force influence index value”, a difference, a ratio, or the like between “correction displacement” and “non-correction displacement” may be employed as described in the section of the embodiment described later. Alternatively, the ratio of “uncorrected displacement” to “corrected displacement” at any given part of the structure multiplied by “corrected displacement” at another part of the structure and “non-corrected displacement” at the other part of the structure. Differences, ratios, etc. from the value of “corrected displacement” may be calculated as the guidance force influence index value. In this case, the influence of the guiding force of another part on a certain part can be relatively grasped, which is advantageous.

  In the embodiment of the numerical analysis device of the present invention, the distribution of the “inductive force vector” and the distribution of the “inductive force influence index value” in the structure are prepared, and the distribution is output or graphically displayed. May be displayed. In addition, as a part of a device that performs numerical analysis by a finite element method or the like and calculates stress and displacement of each analysis element, a device that calculates “inductive force vector” and “inductive force influence index value” according to the present invention May be incorporated.

  According to the present invention, when the numerical analysis of the mechanical characteristics of the structure forming the shell structure is performed according to the finite element method, another of the above problems is the structure of the structure using a computer according to the finite element method. A numerical analysis device for mechanical characteristics, in a numerical model assuming a shell structure of a structure having a plurality of analysis elements, a load applied to the structure and a structure generated when the load is applied Use the influence variable matrix to calculate the displacement of each analysis element, or the displacement of each analysis element calculated using the load and the influence variable matrix, the stiffness matrix of the analysis element, and the curvature matrix of the analysis element Means for calculating an induced force vector acting in a direction different from the direction of the load in each analysis element when a load is applied to the structure, and means for outputting or displaying the induced force vector. Including equipment Thus it is achieved.

  When numerical analysis of the mechanical properties of a structure is performed according to the finite element method, in general, in a numerical model of a structure, each displacement of an analysis element when a certain load is applied is represented by the load and the structure. The stress is determined by using the influence variable matrix according to the structure of the numerical model of the body, and further using the displacement and the stiffness matrix determined by the numerical model of the structure. On the other hand, the inductive force vector is determined based on the stress of each analysis element. As will be described later in the section of the embodiment, the inductive force vector is determined in a numerical model assuming a shell structure. In this case, it can also be expressed by a curvature matrix of an analysis element and a stress tensor. Then, when the finite element method is executed in the numerical analysis of the mechanical characteristics of the structure, the induction force vector is directly calculated when the load applied to the structure and the load are applied. The displacement and stiffness matrix of each of the analysis elements calculated using the influence variable matrix, stiffness matrix, and curvature matrix that calculate the displacement of each analysis element of the resulting structure, or using the load and the influence variable matrix And the curvature matrix can be calculated, and the stress of the analysis element need not be calculated explicitly.

  Thus, according to the present invention described above, in one aspect, in the numerical analysis of the mechanical characteristics of the structure, the structure is applied with a load in a direction different from the direction of the load. An index value representing the influence of the induced force vector is calculated and can be output or displayed. Referring to the induction force vector and the induction force influence index value, the structure or the area where the function of transmitting a given load is not exhibited and the degree thereof are grasped, and the induction force vector and the induction force are determined. By comparing the magnitude or distribution of the force influence index value with the shape of the structure, it is useful information for estimating whether or not a certain part is easily deformed or a part or region that is easily deformed. And by using such information, in order to enable the function to transmit the load to a part or region where the function to transmit the load is not exhibited, or to prevent deformation, It is expected that the design change of the structure such as reinforcement becomes easier.

  Other objects and advantages of the present invention will become apparent from the following description of preferred embodiments of the present invention.

FIG. 1 is a diagram schematically showing a computer on which numerical analysis of the mechanical properties of a structure according to the present invention is executed. FIG. 2A is a schematic diagram showing a state where a load F is applied to a linear structure, and FIG. 2B is a schematic diagram showing a state where a load F is applied to a curved structure. It is. FIG. 2C is a diagram schematically showing the state of the force generated in the structure when a load is applied in the direction of increasing the curvature in the curved structure. FIG. 3 is a schematic diagram of a lattice model of a structure that is divided into elements along the xyz-axis direction in which the numerical analysis of stress is performed, and schematically illustrates the directions of the principal axes x1-x2-x3 calculated by the stress analysis. It shows. FIGS. 4A and 4B are diagrams illustrating a method for determining an induction force when stress in the thickness direction is not calculated in a curved structure. FIG. 5 shows an example of the distribution of induced force vectors calculated when a bending load is applied to the H-shaped beam-shaped member curved from the beginning illustrated in FIG. FIG. 6A is a schematic diagram of an analysis element in the finite element method when a shell structure is used as a numerical model of the structure, and FIG. 6B is a calculation at a node of the analysis element. It is a figure explaining the calculation method of the induced force vector performed. FIG. 7A is a diagram schematically showing a displacement mode when a load is applied to a part of a certain structure, and FIG. 7B shows the structure of FIG. FIG. 5 is a diagram schematically showing a displacement mode when an induced force vector is subtracted from a load applied so that the induced force is canceled. FIG. 7C is a diagram comparing the structure after displacement in the case of (A) and the structure after displacement in the case of (B). FIG. 8A is a schematic diagram of an H-shaped beam-like member that is bent from the beginning to give a bending load in numerical analysis, and FIG. 8B is a deformed state obtained by deformation analysis. It is a schematic diagram of this H-shaped beam-shaped member. The shading in the figure indicates the magnitude of the stress, and the darker the stress is. FIG. 8C is a schematic diagram of a cross section of a deformed H-shaped beam-like member, and shows a state in which both edges of the upper and lower plate-like portions are curved in a direction close to each other.

DESCRIPTION OF SYMBOLS 1 ... Computer body 2 ... Computer terminal 3 ... Monitor 4 ... Keyboard, mouse (input device)

Arrangement of Computer Device A numerical analysis device for the mechanical properties of a structure according to the present invention is of the type normally used in this field, as illustrated in FIG. 1 (A). It may be realized by operating a program. The computer apparatus 1 is equipped with a CPU, a storage device, and an input / output device (I / O) connected to each other by a bidirectional common bus in a normal manner, and the storage device is used in the calculation of the present invention. A memory storing each program for executing the arithmetic processing, and a work memory and a data memory used during the calculation. In addition, the display and output of instructions, calculation results, and other information to the computer device 1 by the practitioner are performed through the computer terminal device 2 connected to the computer device 1. The computer terminal device 2 is provided with an input device 4 such as a monitor 3 and a keyboard and a mouse in a normal manner. When the program is started, the practitioner inputs according to the display on the monitor 3 according to the program procedure. It is possible to perform various instructions and inputs to the computer apparatus 1 using the apparatus 4 and to visually check the calculation state and calculation result from the computer apparatus 1 on the monitor 3. Note that the computer device 1 and the computer terminal device 2 may be equipped with other peripheral devices (not shown) (printer for outputting results, storage device for inputting / outputting calculation conditions and calculation result information, etc.). Should be understood. When various processes or operations described below are executed using the computer apparatus 1, programs necessary for the various processes or calculations are started in a normal manner, and the practitioner can connect the computer terminal apparatus 2 to the computer terminal apparatus 2. Then, in accordance with the input procedure prepared in the program, data necessary for calculation, calculation conditions at the time of calculation, and other various settings are input, and calculation is started. Then, during or after the execution of the calculation, the calculation result can be output through the computer terminal device 2 as appropriate.

  When calculating the “inductive force vector” and / or “inductive force influence index value” of the structure according to the present invention in the computer apparatus 1 described above, briefly, prior to that, first, the structure Numerical model data, that is, dynamics of a material such as coordinate value data representing the shape of a structure in a certain coordinate space, for example, the (x, y, z) direction of three-dimensional space coordinates, and elastic properties of the structure The data of the physical characteristics is input, and then, numerical analysis of the mechanical characteristics of the structure is typically performed by the finite element method. In the finite element method, as is well known, a structure represented as a numerical model is divided into a plurality of analysis elements of triangles or quadrangles, and an arbitrary load is applied to the nodes of any analysis element of the structure. Data such as stress and displacement of each element when given is calculated. Typically, the data of each element calculated here is specifically the stress value, principal stress value, coordinate expressed in the component in the coordinate space (input coordinate system) when inputting the numerical model. It may be a data group consisting of principal axis directions (principal stress directions) with respect to space, and when calculating an “inductive force influence index value” to be described later, a coordinate space when inputting a numerical model is further included. It may be a data group composed of displacement values of the nodes represented by components in the (input coordinate system). Then, using the data group obtained by these finite element methods, the magnitude and direction of “guidance force vector” and / or “guidance force influence index value” described later are calculated. The induction force vector may be represented by a component in an arbitrary coordinate system. Typically, in the case of a general structure, it may be represented by a component in the coordinate system in the principal axis direction. In the case of a shell structure, it may be represented by a component in a direction perpendicular to the shell surface. In addition, the guidance force vector may be displayed as a vector (arrow) indicating the magnitude and direction on each element of the numerical model of the structure graphically displayed on the monitor 3 as in an example described later. When calculating the inductive force influence index value, the structure after deformation when the load is applied (when the inductive force vector is generated as it is and / or when the inductive force is removed), that is, the displacement becomes the shape. A graphic display of the reflected structure may be displayed on the monitor 3.

Definition and Physical Meaning of Inductive Force Vector With reference to FIG. 2 (A), a load F (a tensile load in the illustrated case) was applied to the linear member as shown in the extending direction. At this time, a force T (tension in the illustrated case) acts in the same direction as the load F inside the member. That is, in this case, the member has a structure to which the load F is transmitted. In other words, it can be said that the member has a function of transmitting the load. On the other hand, when a load F is applied to the curved member as illustrated in FIG. 2B in the extending direction (assuming that the position of the member in the vertical direction on the paper surface is constrained). When looking at a certain point (black dot) inside the member, since the direction of the force T is not opposite, a force S having a direction different from the load F acts as a resultant force. When the member is deformed by the action of the force S, the member is stretched and applied with tension as depicted by a dotted line in FIG. 2B, so that it does not contribute to the transmission of the load F. Thus, it can be said that the inside of the member is in a state where the function of transmitting a load is not achieved. This can also be expressed as “power escapes”. That is, when a load is applied to a certain structure, the load is transmitted in the structure by referring to the magnitude of the force S acting in a direction different from the load F as in the above example. It is possible to specify the position or size of the part or region that does not fulfill the function and the direction and size of the force acting there. In a portion where such force escape occurs, it is possible to significantly improve the rigidity and strength of the structure by adding a member that receives the force S and prevents deformation. In the present invention, the force S having a direction different from the applied load as described above is referred to as an “inductive force vector”. That is, if it is possible to identify the location where the force escapes due to the induced force and the deformation caused by the induced force, the designer can easily propose a design change that improves the structure based on this information.

Therefore, first, an “inductive force vector” is defined in a general structure. Referring to FIG. 2C, in one minute region in the structure, with respect to the direction of one main axis x1, a stress σ1 acts on the lower surface in the drawing and the stress σ1 + ∂σ1 / acts on the upper surface. Consider the case where ∂x1 · dx1 acts. 2B, the tension T resulting from the load F acts from both sides as shown in FIG. 2B, and the component of the force in the direction of the main axis x1, that is, the component of the induced force vector is expressed as -S. If / 2, the balance of force is expressed by the following formula.
σ1 + ∂σ1 / ∂x1 · dx1−σ1 + 2 · S / 2 = 0 (1)
Therefore, the component S of the inductive force vector is
S = − (∂σ1 / ∂x1) · dx1 (2)
It becomes. Furthermore, in terms of the component I1 of force per volume,
I1 = − (∂σ1 / ∂x1) (3)
Is obtained. Since the relational expression of the expression (3) is also established in the other two principal axis directions in the solid as shown in FIG. 3, the induction force vector I is defined by the following expression. .
Here, e1, e2, and e3 are unit vectors in the principal axis directions x1, x2, and x3, respectively.

Further, when the structure to be analyzed is a shell structure, if the x3 direction is the thickness direction perpendicular to the surface of the shell and the x1 and x2 directions are the extending direction of the shell surface, σ3 is the thickness direction. The median value (in the finite element method, the average value of the stresses on the front and back surfaces) is used, and the differential value of σ3 cannot be calculated. In that case, the following force balance formula:
(4) can be rewritten into the following equation using
Here, τ13 and τ23 are shear stresses in the x3 direction on the surfaces facing the x1 and x2 directions. When the shell surface is a curved surface, the direction of the shell surface changes depending on the location, and the direction of the coordinate axis differs depending on the location. Therefore, even when σ3 calculated by the finite element method is 0, τ13 and τ23 are 0. Must not. Thus, if the direction of x1 is an angle θ in the vicinity C of the center point O in FIG. 4, the value of τ13 of the point C in the coordinate system of the point O is
τ13 = cosθsinθ · σ1 to θ · σ1 (7)
It becomes. Further, if the distance between OCs is Δx, R = Δx / θ (8) between the radius of curvature R in the x direction of the shell and the angle θ.
The derivative of τ13 can be approximated by a difference,
∂τ13 / ∂x1
˜ {τ13 _{(point C)} −τ13 _{(point O)} } / Δx = τ13 _{(point C)} / Δx (9)
Given by. Generalizing the above consideration, the stress σij in the extending direction of the surface (i, j = x or y; in the finite element method, the average value of the stress on the surface and the back surface) and the resulting induced force vector component The relationship with the component perpendicular to the shell surface (direction of e3) Fn (i, j) is understood from FIG.
Fn (i, j) = σij / Rij (10)
It becomes. Here, since the formula (10) is generalized, the directions of x and y do not need to be the principal axis direction of stress, and may be an arbitrary coordinate system taken in the extending direction of the shell surface. Rij has components R11 (Rxx), R12 (Rxy), R21 (Ryx), and R22 (Ryy), R11 is a radius of curvature along a line along the x direction of the shell surface, and R22 is in the y direction of the shell surface. The radius of curvature on the line along the line, R12, is the difference between the radius of curvature on the line along the x = y direction of the shell surface and the radius of curvature on the line along the x = -y direction, and R21 = R12. Therefore, in the curved piece of the shell structure schematically illustrated in FIG. 4B, the component Fn of the induction force vector in the thickness direction is the component of the stress σij in the extending direction of all the surfaces. Because it becomes sum,
Fn = σxx / Rxx + σyy / Ryy + 2σxy / Rxy (11)
It will be represented by. Here, as shown in FIG. 4B, Rxx, Ryy, and Rxy are the curvature radii of the curved surface pieces at the sites where the stress σij acts (from the balance of stress, σxy = σyx Yes, Rxy = Ryx due to symmetry) In the above equation (6), 1 / Rxx, 1 / Ryy, and 1 / Rxy are components of the curvature matrix Qij in the curved piece, respectively. The component in the thickness direction of the force vector is calculated using the curvature matrix Qij and the stress tensor σij (i, j = x, y)
Fn = Σ _i Σ _j Q _ij σ _ij (A)
(Here, Σ _i and Σ _j represent the sum of i and j.)
Is calculated by The calculation shown here can be performed for each element, each contact, or both, and the object of the present invention can be achieved by either method.

Calculation of Inductive Force Vector The inductive force vectors I and Fn are calculated using stress value data obtained by the finite element method. When the structure is a solid as illustrated in FIG. 3 and the equation (4) is used as the equation of the induction force vector I, the x1, x2, and x3 directions (the principal axis direction) in the equation of the induction force vector I are used. For example, in each element, the differential value of the principal stress may be calculated from the difference between the adjacent elements and the distances Δx, Δy, Δz between the elements using a method such as a least square method. In the calculation for one element, the number of adjacent elements is up to 26 including the thickness direction (not shown), and how many of them are used for calculation is arbitrary and wider. You may calculate including the elements of the range. When the structure has a shell structure, the component Fn in the direction perpendicular to the surface (thickness direction) is particularly important among the induction force vectors. This is because a force perpendicular to the surface can easily deform the shell structure, so that the above-described phenomenon that the force escapes easily occurs. When Expression (A) is used as the expression of the component Fn in the thickness direction of the induction force vector, the curvature matrix component Q _ij may be calculated by, for example, the technique described in Patent Document 5.

  FIG. 5 shows an example of the distribution of induced force vectors calculated when a bending load is applied to the H-shaped beam-shaped member of FIG. Referring to the figure, the inductive force vectors are directed toward each other in the upper and lower plate members, and increase in size between the center line of the upper and lower plate members and the middle of both edges parallel thereto. Is understood. When the distribution of the induction force vector is compared with the graphic display of the deformation analysis in FIG. 8B, as already mentioned, the upper and lower plate members are curved in directions in which both edges are directed toward each other, and the direction of the induction force vector is To be understood. Thus, by referring to the induction force vector, a force in a direction different from the load transmission direction acts on the middle line between the center line of the upper and lower plate members and both edges parallel to the center line. It is possible to consider the reason that the contribution of the transmission of the moment) is small and the bending in a direction different from the applied load transmission direction occurs.

Calculation of the guiding force effect index value As described above, when the distribution of the guiding force vector is obtained, it is possible to consider the region where the bending in a direction different from the applied load occurs. It is expected that the influence or contribution to can be grasped more clearly by observing the state of the structure after deformation in the presence and absence of the inductive force vector. Therefore, in the apparatus of the present invention, the calculation of the guidance force vector, the displacement of each element of the structure in the state where the guidance force vector exists (uncorrected displacement), and the guidance force vector do not exist. The displacement (corrected displacement) of each analysis element of the structure in the state is calculated. Then, in order to compare the uncorrected displacement with the corrected displacement and consider the contribution of the induced force vector, the “inductive force effect index value” based on the uncorrected displacement and the corrected displacement, ie, the contribution of the induced force vector An index value representing is calculated.

  Specifically, first, the calculation of the induction force vector is performed as described above, and the uncorrected displacement of each element of the structure in the state where the induction force vector exists, the load is structured in the normal manner. It may be calculated according to the finite element method in a state applied to any part of the body.

Regarding the corrected displacement of each element of the structure in the state where no induction force vector exists, each element of the structure is obtained by subtracting the induction force vector from the load in the state where the induction force vector exists. The displacement of is calculated. More specifically, first, when the induction force vector of each analysis element when a certain load is applied to the structure is calculated, the induction is performed from the load (vector) applied to each node of each analysis element. The force vector is subtracted. It should be noted that at the node where no load is applied in the calculation of the previous induction force vector and the displacement of the structure, an amount corresponding to the magnitude of the induction force vector is subtracted from the state where the load = 0. Become. In particular, when the structure has a shell structure as shown in FIG. 6A, the following correction load P _i ^* is applied to each node i.
P _i ^* = P _i −f _i (12)
Here, i is a symbol of the node, and P _i is a load applied to each node when the induction force vector is calculated (thus, in a node to which no load is applied, P _i = 0.) f _i is an inductive force vector component acting on each node (that is, subtraction of the inductive force vector component may be performed only in the thickness direction in the case of a shell structure). When the inductive force vector is calculated only for each element a 1, when calculating the corrected load P _i ^* of the equation (7) for each node, as shown in FIG. The average value of the induction force vector calculated by the analysis element to which the node belongs may be used as f _i . That is, the component f _i of the induction force vector at each node is
f _i = (1 / N _i ) ΣF _n ^a V ^a (13)
Given by. Here, N _i is the number of analysis elements to which the node i belongs, a is a sign of the analysis element, F _n ^a is an induction force vector component in the thickness direction of the analysis element a, and V ^a is the volume (area × thickness) of the analysis element a, and Σ is the sum of the values for the analysis element to which the node i belongs. Then, the displacement of each element of the structure may be calculated according to the finite element method in a normal manner in a state where the correction load P _i ^* according to Expression (7) is applied.

  FIG. 7 schematically shows the state of the structure when the above-described series of processing is executed. Referring to FIG. 7A, in FIG. 7A, in a state where a load is applied to a certain analysis member, an induction force vector distribution (left diagram) and a displacement of the structure after deformation ( (Right figure) is calculated. Then, in the structure after deformation, there is a case where a region that deforms in a direction different from the load transmission direction (a part surrounded by a dotted line in the figure) corresponding to the induced force vector distribution may occur. is there. Such deformation of the region is caused by the induced force vector, and it is expected that a phenomenon in which the force escapes occurs. Therefore, as illustrated in FIG. 7B, the displacement of the structure after deformation (right diagram) is calculated in a state where a load is applied so as to cancel out the induction force vector (left diagram). The In that case, in the region where the force escape occurs in FIG. 7A, it is expected that a change such as disappearance of the force escape occurs due to the effect of canceling the induced force vector. Thus, as depicted in FIG. 7C, by comparing the structure state (A) before the load correction and the structure state (B) after the load correction, the inductive force The influence or contribution of the vector can be understood more clearly. In a normal structural analysis, the displacement is very small compared to the size of the structure, and the influence of the change in shape due to the displacement is often negligible. In the present invention, both the uncorrected displacement and the modified displacement are considered to be very small, and the deformation is enlarged and displayed in FIGS. 7 and 8 for explanation. When deformation cannot be ignored, it is generally said that a structural model is recreated from a slightly deformed shape, and analysis is performed on the reconstructed structure, and finally analysis for large deformation is performed. The same method can be used in the present invention.

In the comparison between the state (A) of the structure before correction of the load and the state (B) of the structure after correction of the load as illustrated in FIG. It is difficult to quantitatively grasp the influence of the induction force vector only by comparing and observing the shape of the structure. Therefore, in the apparatus of the present invention, as described above, the “induction force effect index value” is calculated based on the uncorrected displacement and the corrected displacement. Specifically, the uncorrected displacement ui of each node of the structure in the state where the induction force vector exists, and the corrected displacement ui ^* of each node of the structure in the state where the induction force vector does not exist The difference between them,
βi = ui-ui ^* (14a)
Their ratio,
γi = ui / ui ^* (14b)
Etc. may be calculated for each node. Alternatively, the following correction coefficients are used for an uncorrected displacement ui and a corrected displacement ui ^* of an arbitrary partial region of the structure, for example, a region to which a significant load is applied (region surrounded by T in the figure). λ ^T is defined,
λ ^T = Σui / Σui ^* (15)
(Where Σ is the sum in the region τ),
Further, the following degree of influence βi ^τ may be calculated.
βi ^T = (ui−λ ^T ui ^* ) (16a)
Or ^{βi T = (ui-λ T} ui *) · f i ... (16b)
Here, · represents an inner product of vectors.
In the above formula (11a, b), (ui−λ ^T ui ^* ) is expected to be substantially 0 in the region T, while other than the region T. In the region where the guiding force vector exists, the difference due to the presence or absence becomes remarkable, which is advantageous for more clearly grasping the contribution of the guiding force vector. Selection of region T, so that the value of the existing areas or as a value of at .beta.i ^T increases a significant induction force in .beta.i ^T to nonexistent region Vector significant induction force vector is reduced May be appropriately selected. The above β i, γ i, β i ^T may be displayed on the monitor 3 together with the graphic display of the structure.

Another Embodiment of Calculation of Inductive Force Vector As already described, when the structure has a shell structure, the inductive force vector is calculated by the curvature matrix Qij and the stress tensor σij according to the equation (A). Regarding this point, in the numerical analysis by the finite element method, the stress tensor σij of each node is expressed by using the stiffness matrix S and the displacement vector ui as follows: σij = S · ui
The displacement vector ui is calculated using the load vector Pi of each node and the influence variable matrix K,
ui = K ・ Pi
It is calculated in the form of Here, the calculation of the expression (A) is performed as follows: Q * σ = Σ _i Σ _j Q _ij σ _ij (A)
Inductive force vector Fn is expressed as
Fn = Q * S · ui (17a)
Fn = Q * S · K · Pi (17b)
Given by. Since the stiffness matrix S and the influence variable matrix K are determined by setting a numerical model, the induction force vector is directly calculated from the displacement vector ui or directly from the load vector Pi without calculating the stress explicitly. May be. Note that the induced force vector calculated in this case is a component of the induced force vector after deformation of the structure.

  Although the above description has been made in relation to the embodiment of the present invention, many modifications and changes can be easily made by those skilled in the art, and the present invention is limited to the embodiment exemplified above. It will be apparent that the invention is not limited and applies to various devices without departing from the inventive concept.

Claims (2)

A numerical analysis device for mechanical properties of a structure using a computer,
In a numerical model of the structure having a plurality of analysis elements, when a load is applied to the structure, an induction force vector acting in a direction different from the direction of the load is applied to each of the analysis elements. Means for calculating;
Means for calculating an uncorrected displacement generated in each of the analysis elements when the load is applied to the structure in the numerical model of the structure;
Means for calculating a correction load generated in each of the analysis elements when a correction load obtained by subtracting the induction force vector from the load is applied to the structure in the numerical model of the structure; ,
Means for calculating an index value representing the contribution of the induced force vector based on the uncorrected displacement and the modified displacement in each of the analysis elements; and outputting or displaying the index value representing the contribution of the induced force vector Means comprising: A numerical analysis device for mechanical properties of a structure using a computer according to a finite element method,
In a numerical model assuming a shell structure of the structure having a plurality of analysis elements, the load applied to the structure and the displacement of each analysis element of the structure that occurs when the load is applied are calculated. The structure using the displacement of each analysis element calculated using the influence variable matrix or the load and the influence variable matrix, the stiffness matrix of the analysis element, and the curvature matrix of the analysis element Means for calculating an inductive force vector acting in a direction different from the direction of the load in each of the analysis elements when a load is applied to
Means for outputting or displaying said inductive force vector.